WMOD00473

• Title: Evaluation of Bridger Range Winter Cloud Seeding Experiment Using Control Gages
• Date: 12/12/1983
• Weather Modification - Doc Type: Report

DECEMBER 1983

ARLIN B. SUPER AND JAMES A. HEIMBACH, JR.

1997

By the final winter season (1971-72), plume tracing
and airflow observations suggested there was little need
for the buffer period. A random decision was then
assigned to each calendar date prior to the start of the
season by Dr. Paul Mielke ofCSU. The randomization
was restricted to no more than three seed or nonseed
decisions in a row. With the exception that some blocks
of days were set aside from the randomized experiment
for special experiments at least 6 days in advance (see
Part I), each experimental day was declared solely on
the NWS special forecast. That is, each day forecast
to have a greater than 20% probability of precipitation
at the Bozeman Airport was an experimental day.
Rawinsonde launches were scheduled four times per
experimental day, at 1500, 2100, 0300 and 0900.
However, available resources required compromise
with the ideal of 4 launches per day whatever the
weather. Instead, rawinsondes were launched when
PSC, as defined above, existed approximately 1 h before
the scheduled release time.
A total of 364 usable rawinsonde observations were
obtained during the two winters being considered. Most
6 h periods with snowfall in the intended target area
have accompanying rawin data. To illustrate, let it be
assumed that at least 3 of 12 gages in Zone 1 of Fig.
1 must register ;>0.02 inches for a significant snowfall
event to have occurred in a 6 h period centered on a
potential rawin launch time. This should largely elim-
inate cases with apparent but questionable snowfall
episodes. Such occurrences may be due to gage mech-
anism expansion/contraction, snow adhering to the
inside orifice wall and finally falling off, etc. A total
of 319 6 h periods met these criteria out of the total
of 740 possible (185 X 4). Soundings exist for 253
(79%) of these 319 periods. Considering the entire ex-
perimental day, only 9 had a significant snowfall event
as defined, but no rawinsonde observations. Thus, the
procedures used were reasonably successful in provid-
ing upper air data for partitioning the experimental
units.

6. Statistical techniques

Earlier analysis of the BRE, referenced in Section
1, suggested that type I errors existed in the data pool.
In that analysis, the seeded and nonseeded precipitation
accumulations at each individual gage were compared
using the Wilcoxon rank-sum (Mann and Whitney,
1947) and the squared-rank-sum tests (Noether, 1967).
Mielke, et at. (1981a) applied a nonparametric in-
ference technique in a reanalysis of Climax I and II.
In their study, rank-ordered residuals from a linear
least-squares line (y = bx) fitted to paired target-control
observations, were input to two-sample rank-sum tests.
This approach compensated for covariate data. How-
ever, Mielke et at. (1982), noted that the least-squares
inference can place undue weight on the outlying data
pairs and there is potential for distortion in the Wil-

..J

coxon rank-sum test due to its non-Euclidean geom-
etry. They applied a new nonparametric inference
technique to the Climax data to reduce distortions.
Residuals were found using the median regression line
and testing was through the multiresponse permutation
procedures (MRPP).
In the analysis herein both the well-known Wilcoxon
rank-sum and the MRPP are used to test for differences
in the rank-ordered target residuals determined from
the median regression line. Following Mielke et at.
(1982), the median regression line is forced through
the origin to minimize the impact of "busted" forecasts
and the number of cases when either the target or
control, but not both, had zero precipitation. The
seeded and nonseeded target control pairs were pooled
to define the median line. Only those pairs meeting
partition criteria were applied. Although the possibility
of distortion apparently exists for the Wilcoxon test
(Mielke et at., 1982), it is kept in this analysis because
it is particularly well-known. The MRPP is a new ap-
proach which has yet to stand the test of time; however,
since it is .able to perform multiresponse analyses ef-
ficiently, its utilization will likely increase with time.
A complete description ofMRPP and efficient com-
putation techniques is given by Mielke et at. (1976)
and an easily understood example is presented by
Mielke et at. (1981 b). For this study, there is only one
response variable which is the residual from the median
line. The statistic 0 is found using the differences be-
tween the residuals to the unit power; i.e., Euclidean
distance (k = 1 of Mielke et at., 1976) is inferred. There
are two groups, of sizes ns and nn, corresponding to
seeded and nonseeded samples. The effect of outlying
residuals is minimized by substituting a score function
for the residuals in MRPP. The Ith score function Sf,
is derived from the tie-adjusted ranks of the residuals

S[ = rank[ - (ns + nn + 1)/2. (1)

This was applied by Mielke et at., (1981a) and Mielke
et at. (1982).
A generalized Fortran program to apply MRPP was
provided by P. Mielke and adapted to a Perkin-Elmer
3220 computer. Running this test required that large
amounts of data be input and output to a temporary
disc file. The resulting long run-times forced the use
of the Wilcoxon as a screening test for preliminary
analysis.
In this analysis partitions yielding less than ns + nn
= 20 samples were not considered because the null
distributions of the test statistic may not be adequately
approximated by a standardized variable. For example,
Mann and Whitney (1947) suggested that about eight
samples for each of two random variables are required
in the Wilcoxon rank-sum test for the ranks of ob-
servations to be approximately normal.
It is of obvious interest. to consider the magnitude
of the precipitation differences betWeen the seeded and